Timeline for Why different noise terms are read at specific sampling interval in Allan Variance plot?
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| Jan 17 at 13:03 | comment | added | Dan Boschen | Here is the link to the other post I mentioned demonstrating the same waveform transitioning from constant mean white noise to random walk: dsp.stackexchange.com/questions/91692/… . I also rephrased my answer as you are technically not incorrect referring to $\tau$ as the sampling interval as it will still work if you sample properly (boxcar avg first), but it can be misleading and "averaging interval" is much clearer to me in its use, purpose and computation. | |
| Jan 17 at 13:00 | comment | added | Dan Boschen | (My current day job is designing atomic clocks so I am familiar with this from that regard - we spend a lot of effort to make frequency sources that will have frequency noise that maintains itself as white noise for VERY long time intervals-- so a higher quality device such that the random walk noise (due to eventual drift as all things will) occurs at much higher taus. That is what I mean by higher quality device. | |
| Jan 17 at 12:58 | comment | added | Dan Boschen | For that particular plot, that is where those noise types were dominant (based on the slope in the curve itself). Why this happens is based on the quality of the device. I have another recent post that demonstrates a process that is drifting long term, but if we only observe over short intervals it would appear (and mathematically be equivalent) to be stationary constant mean white Gaussian noise. I'll add the link to that. | |
| Jan 17 at 12:55 | comment | added | Mahesha999 | [...continued] Also, I know that those different noise processes does not occur at specific $\tau$ but over a range of $\tau$. My question was why all articles / tutorials ask to measure these different noises at specific $\tau$. For example this comment asks to read white noise at $\tau=1$ and random walk at $\tau=3$. Page 30 of pdf stated in earlier comment asks to read quantization noise at $\tau=\sqrt{3}$ and random walk at $\tau=3$. Why is this so? | |
| Jan 17 at 12:55 | comment | added | Mahesha999 | Aah, I miss used the term "sampling time". I indeed mean "averaging time". Correct me again if am wrong: sampling time is how frequently we obtain readings from the sensor. $$\text{Averaging time} = \text{number of samples in cluster used to calculate AVAR} \times \text{sampling time}$$ [ page 28 of this pdf ]. [continued ...] | |
| Jan 17 at 12:50 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Jan 17 at 6:03 | history | edited | Dan Boschen | CC BY-SA 4.0 |
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| Jan 17 at 5:44 | history | answered | Dan Boschen | CC BY-SA 4.0 |